1,721,245 research outputs found
Disturbance attenuation in nonlinear perturbed diffusion processes by sampled-in-space sensing and actuation
No full textA diffusion equation perturbed by uncertain disturbances
of both matching and unmatching nature is considered.
The problem of disturbance attenuation is tackled by
means of the sliding-mode control approach. It is assumed that
only a finite number of pointwise sensing and actuation devices,
suitably located in an equi-spaced manner along the spatial
domain of interest, is available. We show that an arbitrary level
of the unmatching disturbance attenuation can be achieved by
employing a sufficiently high number of sensing and actuation
devices. We also show that matching disturbances entering the
control channels can be fully rejected by the proposed design
Leader-follower synchronization and ISS analysis for a network of boundary-controlled wave PDEs
Full text linkA network of agents, modeled by a class of wave PDEs, is under investigation. One agent in the network plays the role of a leader, and all the remaining 'follower' agents are required to asymptotically track the state of the leader. Only boundary sensing of the agent's state is assumed, and each agent is controlled through the boundary by Neumann-type actuation. A linear interaction protocol is proposed and analyzed by means of a Lyapunov-based approach. A simple set of tuning rules, guaranteeing the exponential achievement of synchronization, is obtained. In addition, an exponential ISS relation, characterizing the effects on the tracking accuracy of boundary and in-domain disturbances, is derived for the closed loop system
BOUNDARY SECOND-ORDER SLIDING-MODE CONTROL OF AN UNCERTAIN HEAT PROCESS WITH UNBOUNDED MATCHED PERTURBATION
No full textThe primary concern of the present paper is the regulation of an uncertain heat process with collocated boundary sensing and actuation. The underlying heat process is governed by an uncertain parabolic partial differential equation (PDE) with Neumann boundary conditions. It exhibits an unknown constant diffusivity parameter and it is affected by a smooth boundary disturbance, which is not available for measurements and which is possibly unbounded in magnitude. The proposed robust synthesis is formed by the linear feedback design and by the "Twisting" second-order sliding-mode control algorithm, suitably combined and re-worked in the infinite-dimensional setting. A non-standard Lyapunov functional is invoked to establish the global asymptotic stability in a Sobolev space, involving spatial state derivatives of the same order as that of the plant equation. The stability proof is accompanied by a set of simple tuning rules for the controller parameters. The effectiveness of the developed control scheme is supported by simulation results
Muon revolution frequency distribution from a partial-time Fourier transform of the g-2 signal in the muon g-2 experiment
No full textA new method of precise measurement of the revolution frequency distribution, F(f), in the muon storage ring, and hence muon momentum p, energy E, and equilibrium radius R distributions, has been developed and used in analyzing data in the muon g-2 experiment at Brookhaven National Laboratory. The method is partly based on the Fourier transform of the observed electron decay signal, which is known in this experiment only after some time t(s) after injection. It is shown that the standard Fourier transform would give a wrong frequency distribution even if the signal were known immediately after injection. Only the cosine Fourier transform with the property determined initial time t(0) (different for different detectors placed along the orbit) gives the correct frequency distribution in such a case. As for a later starting time, t(s) > t(0), a special procedure must be used to find t(0) and to compensate for the lack of information about the signal between t(0) and t(s). The new technique is highly accurate and radically different from that used by CERN in its muon g-2 experiment. (C) 2002 Elsevier Science B.V. All rights reserved
Boundary control of coupled reaction-diffusion processes with constant parameters
Full text linkThe problem of boundary stabilization is considered for some classes of coupled parabolic linear PDEs
of the reaction–diffusion type. With reference to n coupled equations, each one equipped with a scalar
boundary control input, a state feedback law is designed with actuation at only one end of the domain, and
exponential stability of the closed-loop system is proven. The treatment is addressed separately for the
case in which all processes have the same diffusivity and for the more challenging scenario where each
process has its own diffusivity and a different solution approach has to be taken. The backstepping method
is used for controller design, and, particularly, the kernel matrix of the transformation is derived in explicit
form of series of Bessel-like matrix functions by using the method of successive approximations to solve
the corresponding PDE. Thus, the proposed control laws become available in explicit form. Additionally,
the stabilization of an underactuated system of two coupled reaction–diffusion processes is tackled under
the restriction that only a scalar boundary input is available. Capabilities of the proposed synthesis and its
effectiveness are supported by numerical studies made for three coupled systems with distinct diffusivity
parameters and for underactuated linearized dimensionless temperature-concentration dynamics of
a tubular chemical reactor, controlled through a boundary at low fluid superficial velocities when
convection terms become negligibl
Consensus-Based Control for a Network of Diffusion PDEs with Boundary Local Interaction
No full textIn this technical note the problem of driving the state of a network of identical agents, modeled by boundary-controlled heat equations, towards a common steady-state profile is addressed. Decentralized consensus protocols are proposed to address two distinct problems. The first problem is that of steering the states of all agents towards the same constant steady-state profile which corresponds to the spatial average of the agents initial condition. The second problem deals with the case where the controlled boundaries of the agents dynamics are corrupted by additive persistent disturbances. To achieve synchronization between agents, while completely rejecting the effect of the boundary disturbances, a nonlinear sliding-mode based consensus protocol is proposed. Simulation results are presented to support the effectiveness of the proposed algorithms
Lyapunov-based second-order sliding mode control for a class of uncertain reaction-diffusion processes
No full textThis paper addresses the design of a distributed, second-order sliding-mode based, tracking controller for a class of uncertain diffusion-reaction processes. Spatially varying uncertain parameters and mixed boundary conditions, along with the presence of an uncertain distributed disturbance, characterize the considered class of processes. The paper presents a constructive Lyapunov-based stability analysis which leads to simple tuning conditions for the controller parameters, The good performance of the proposed control systems are verified by means of computer simulations
On the Lyapunov-based second-order SMC design for some classes of distributed parameter systems
No full textThis paper addresses the Lyapunov-based design of second-order sliding mode controllers in the domain of distributed parameter systems (DPSs). To the best of our knowledge, the recent authors' publications (Orlov et al., 2010, Continuous state-feedback tracking of an uncertain heat diffusion process. Syst. Control Lett., 59, 754-759; Orlov et al., 2011, Exponential stabilization of the uncertain wave equation via distributed dynamic input extension. IEEE Trans. Autom. Control, 56, 212-217; Pisano et al., 2011, Tracking control of the uncertain heat and wave equation via power-fractional and sliding-mode techniques. SIAM J. Control Optim., 49, 363-382) represent the seminal applications of second-order sliding mode control techniques to DPSs. A Lyapunov-based framework of analysis was found to be appropriate in the above publications. While reviewing the main existing results in this new field of investigation, the paper provides the novelty as well and gives several hints and perspectives for the generalization, listing some open problems
Sliding-mode Boundary Control of Uncertain Reaction-Diffusion Processes with Spatially Varying Parameters
No full textThe primary concern of the present paper is the stabilization problem of a one-dimensional uncertain reaction-diffusion process powered with a Dirichlet type actuator from one of the boundaries. The heat flux at the controlled boundary is the only measured signal, the uncertain diffusion and reaction parameters are admitted to be spatially varying, and the system is also affected by a sufficiently smooth boundary disturbance, which is not available for measurements and can be also unbounded in magnitude. The proposed robust synthesis is based on a dynamic input extension, and it is formed by the relay control algorithm and a linear term, suitably combined. A continuous stabilizing boundary control law is suggested to achieve exponential stability under some restrictions on the uncertain parameters spatial profiles characteristics. A Lyapunov-based functional analysis is invoked to establish the global exponential stability in the Sobolev space W1, 2(0, 1). The proof is accompanied by a set of simple tuning rules for the controller parameters. The effectiveness of the developed control scheme is supported by simulation results
Combined Backstepping/Second-Order Sliding-Mode Boundary Stabilization of an Unstable Reaction-Diffusion Process
Full text linkIn this letter we deal with a class of open-loop unstable reaction-diffusion PDEs with boundary control and Robin-type boundary conditions. A second-order sliding mode algorithm is employed along with the backstepping method to asymptotically stabilize the controlled plant while providing at the same time the rejection of an external persistent boundary disturbance. A constructive Lyapunov analysis supports the presented synthesis, and simulation results are presented to validate the developed approach
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